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The dataset generation failed
Error code:   DatasetGenerationError
Exception:    ArrowInvalid
Message:      Schema at index 1 was different: 
orid: string
arxiv_id: string
title: string
area: string
authors: list<item: string>
arxiv_url: string
openreview_url: string
text_source: string
full_text: bool
vs
n: int64
sigma_sq: double
tau: double
trials: int64
n_partitions_enumerated: int64
exhaustive: bool
rows: list<item: struct<d: int64, frac_fixed: double, sd: double, one_minus_frac: double, eq1_bound: double, lloyd_iters: double, lloyd_err: double, random_init_err: double>>
frac_fixed_at_d16384: double
bound_becomes_informative_at_d: int64
lloyd_err_vs_random_err_highd: list<item: double>
runtime_s: double
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1858, in _prepare_split_single
                  num_examples, num_bytes = writer.finalize()
                                            ~~~~~~~~~~~~~~~^^
                File "/usr/local/lib/python3.14/site-packages/datasets/arrow_writer.py", line 781, in finalize
                  self.write_rows_on_file()
                  ~~~~~~~~~~~~~~~~~~~~~~~^^
                File "/usr/local/lib/python3.14/site-packages/datasets/arrow_writer.py", line 662, in write_rows_on_file
                  table = pa.concat_tables(self.current_rows)
                File "pyarrow/table.pxi", line 6320, in pyarrow.lib.concat_tables
                File "pyarrow/error.pxi", line 155, in pyarrow.lib.pyarrow_internal_check_status
                File "pyarrow/error.pxi", line 92, in pyarrow.lib.check_status
                  raise convert_status(status)
              pyarrow.lib.ArrowInvalid: Schema at index 1 was different: 
              orid: string
              arxiv_id: string
              title: string
              area: string
              authors: list<item: string>
              arxiv_url: string
              openreview_url: string
              text_source: string
              full_text: bool
              vs
              n: int64
              sigma_sq: double
              tau: double
              trials: int64
              n_partitions_enumerated: int64
              exhaustive: bool
              rows: list<item: struct<d: int64, frac_fixed: double, sd: double, one_minus_frac: double, eq1_bound: double, lloyd_iters: double, lloyd_err: double, random_init_err: double>>
              frac_fixed_at_d16384: double
              bound_becomes_informative_at_d: int64
              lloyd_err_vs_random_err_highd: list<item: double>
              runtime_s: double
              
              The above exception was the direct cause of the following exception:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
                  parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
                                                                        ~~~~~~~~~~~~~~~~~~~~~~~~~^
                      builder, max_dataset_size_bytes=max_dataset_size_bytes
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                  )
                  ^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
                  builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
                  ~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1683, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ~~~~~~~~~~~~~~~~~~~~~~~~~~^
                      gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                  ):
                  ^
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1869, in _prepare_split_single
                  raise DatasetGenerationError("An error occurred while generating the dataset") from e
              datasets.exceptions.DatasetGenerationError: An error occurred while generating the dataset

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text
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status
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In the high-noise, high-dimensional regime where σ² > n, Lloyd's k-means algorithm fails catastrophically: essentially every partition of the data becomes a fixed point of the algorithm (Theorem 1.1).
unverified
In the same high-noise regime, Hartigan's k-means algorithm avoids this pathology, having no incorrect fixed points with high probability (Theorem 1.1).
unverified
Corollary 3.8 bounds the probability that any q-approximately balanced partition is not a fixed point of Lloyd's algorithm by 2^n · n · ρ_q^(d/4) (Corollary 3.8).
unverified
Corollary 3.12 bounds the probability that any incorrect partition is a fixed point of Hartigan's algorithm by 2^n · ρ_h^(d/4), a substantially tighter bound than Lloyd's case (Corollary 3.12).
unverified
Theorem 3.4 shows Lloyd's single-sample reassignment step persists misclassification errors once the noise level exceeds σ > (2c̄τ(c−1))/√(c(c+c̄)) (Theorem 3.4).
unverified
Numerical experiments empirically demonstrate the divergence between Lloyd's catastrophic-failure behavior and Hartigan's robustness as dimension grows, corroborating the theoretical bounds (Section 4).
unverified
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